A car dealership sells cars that were made in 2015 through 2020. Let the cars for sale be the domain of a relation R where two cars are related if they were made in the same year.
Describe the partition defined by the equivalence classes.
I am having a difficult time with partitions and equivalence classes, can somebody help me answer this question please?
First of all, you should convince yourself that being produced in the same year is in fact an equivalence relation. Secondly, the equivalence class of a given car consists of all cars produced in the same year. Hence, you get an equivalence class for each year. Here, you actually need to assume that the company has at least one car from each year. With this assumption, the sets in the partition induced by the given equivalence relation are
$$ \{ \text{cars produced in }2015 \}, \{ \text{cars produced in }2016 \}, \cdots, \{ \text{cars produced in }2020 \}.$$